The distance between two towns is 458km.Two trains start from these two stations at the same time and travel towards each other at 45 km per hour and 60km per hour .In how many hours will theybe 38 km apart from each other

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$$\begin{gathered} \mathrm{Total} \mathrm{distance}=458 \mathrm{kms} \\ \mathrm{Speed} \mathrm{of} \mathrm{train} \mathrm{A}=45 \mathrm{km}/\mathrm{hr} \\ \mathrm{Speed} \mathrm{of} \mathrm{train} \mathrm{B}=60 \mathrm{km}/\mathrm{hr} \\ \mathrm{As} \mathrm{trains} \mathrm{are} \mathrm{moving} \mathrm{in} \mathrm{opposite} \mathrm{direction} \mathrm{hence} \mathrm{relative} \mathrm{velocity} \mathrm{will} \mathrm{be} \mathrm{obtained} \\ \mathrm{by} \mathrm{adding} \mathrm{two} \mathrm{velocities}. \\ \Rightarrow \mathrm{v}=60+45=105 \mathrm{km}/\mathrm{hr} \\ \mathrm{Now} \\ \mathrm{As} \mathrm{trains} \mathrm{are} 38 \mathrm{kms} \mathrm{apart}, \mathrm{hence} \\ \mathrm{Relative} \mathrm{distance} \mathrm{travelled}\left(\mathrm{d}\right)=458-38=420 \mathrm{km} \\ \mathrm{Time}\left(\mathrm{t}\right)=\frac{\mathrm{d}}{\mathrm{v}} \\ =\frac{420}{105} \\ =\mathbf{4}\mathbf{ }\mathbf{hours}\mathbf{ }\left(\mathbf{Answer}\right) \end{gathered}$$

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